This is straight from memory so it might not be 100% accurate; I did not try to look it up anywhere.
Let me start by explaining the differences between Automatic and Manual modes, then answer the questions.
Manual mode is similar to driving in previous Mario Kart games. When going around a turn, you can hop and drift to modify the turn. If your drift stays at a sharp enough angle for long enough, the sparks flying out the back of your vehicle will change color. When the color changes, you can release the drift button to get a speed boost.
Automatic mode has none of the hopping or sparks. Instead, it automatically improves your turning by drifting for you and requires a button press. It's probably easier for new players, as they don't need to pay attention to another buttons and the subtleties of maintaining the drift. The downside is you will not build up sparks and will not be able to get the drifting speed boost.
Now let's answer the questions:
- Automatic mode is different, and not really an advantage. It simplifies the driving.
- You can't hop in Automatic mode.
- Yes, both bikes and karts can be driven in automatic mode at the expense of the drift speed boost.
- If you want to improve at the game, I would recommend learning to use manual. The mini-turbos are invaluable for getting and maintaining better speeds. You can drive in manual without doing the drift speed boost, but that's not how you play well!
- If you want to get great times, you will almost certainly want the drift speed boost.
Side note 1: In manual mode, karts (unlike bikes) actually get a second, more powerful level of sparks on drift turns if you wait long enough. Bikes instead get a wheelie speed boost, which you normally want to use on straightaways. (I am not certain whether bikes can wheelie in Automatic mode.)
Side note 2: Different Mario Kart games have different drift-boosting techniques. For example, in Mario Kart 64 and Mario Kart: Double Dash, you actually wanted to alternate steering Left-Right-Left-Right while drifting to get the boost. In Mario Kart Wii, you simply want to maintain a smooth turn that is as sharp as possible.
Edit: With that link to the PDF, I can get the terminology right for the various types of boosts:
- Mini-Turbo - Drifting until sparks appear, then releasing. Only works in Manual mode.
- Super Mini-Turbo - Drifting until orange sparks appear, then releasing. Only works in Manual mode for karts.
- Wheelie - Popping a wheeling on a straightaway. Only works for bikes.
- Tricks - Shaking the controller right when flying off a jump to perform a mid-air trick and gain a speed boost on landing.
This is all on page 7 of the PDF you linked.